Question

The area of a triangle is found by multiplying half of the measure of its base by its height. The area of the following right triangle is 18 square centimeters.

Answer 1

Given:

The triangle is

The area of a triangle is 18 square centimetres.

Find-:

(a)

The value of "h."

Explanation-:

The value of "h" is:

The area of triangles

$\text{ Area }=\frac{1}{2}\times\text{ Base}\times\text{ Height}$

The base is 6 cm

The height is h+1 cm.

The value of "h" is:

$\begin{gathered} \text{ Area }=\frac{1}{2}\times\text{ Base}\times\text{ Height} \\ \\ 18=\frac{1}{2}\times6\times(h+1) \\ \\ 18\times2=6(h+1) \end{gathered}$

The value of "h."

$\begin{gathered} 6(h+1)=18\times2 \\ \\ h+1=\frac{18\times2}{6} \\ \\ h+1=3\times2 \\ \\ h+1=6 \\ \\ h=6-1 \\ \\ h=5 \end{gathered}$

The value of "h" is 5 cm.

(B)

The value of "h" is 5 cm then the area of a triangle is:

$\begin{gathered} \text{ Height }=(h+1)\text{ cm} \\ \\ \text{ Height }=(5+1)\text{ cm} \\ \\ \text{ Height }=6\text{ cm} \end{gathered}$

The area of triangles

$\begin{gathered} \text{ Area }=\frac{1}{2}\times\text{ Base}\times\text{ Height} \\ \\ \text{ Area }=\frac{1}{2}\times6\times6 \\ \\ \text{ Area }=3\times6 \\ \\ \text{ Area }=18\text{ cm}^2 \end{gathered}$